On bivalent semantics and natural deduction for some infectious logics
Logic Journal of the IGPL 30 (1):186-210 (2022)
Abstract
In this work, we propose a variant of so-called informational semantics, a technique elaborated by Voishvillo, for two infectious logics, Deutsch’s |${\mathbf{S}_{\mathbf{fde}}}$| and Szmuc’s |$\mathbf{dS}_{\mathbf{fde}}$|. We show how the machinery of informational semantics can be effectively used to analyse truth and falsity conditions of disjunction and conjunction. Using this technique, it is possible to claim that disjunction and conjunction can be rightfully regarded as such, a claim which was disputed in the recent literature. Both |${\mathbf{S}_{\mathbf{fde}}}$| and |$\mathbf{dS}_{\mathbf{fde}}$| are formalized in terms of natural deduction. This allows us to solve several problems: to develop a natural deduction calculus for |${\mathbf{S}_{\mathbf{fde}}}$| containing the standard form of disjunction elimination (in contrast to the calculus by Petrukhin), to introduce the first natural deduction calculus for |$\mathbf{dS}_{\mathbf{fde}}$| and to reflect the fundamental symmetry between |${\mathbf{S}_{\mathbf{fde}}}$| and |$\mathbf{dS}_{\mathbf{fde}}$| on proof-theoretical level forming a convenient basis for obtaining their well-known extensions |$\mathbf{K}^{\mathbf{w}}_{\mathbf{3}}$| and |$\mathbf{PWK}$|.Author's Profile
DOI
10.1093/jigpal/jzaa071
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References found in this work
What is a Theory of Meaning? (II).Michael Dummett - 1976 - In Gareth Evans & John McDowell (eds.), Truth and Meaning: Essays in Semantics. Oxford: Clarendon Press.
What is a theory of meaning?Michael A. E. Dummett - 1975 - In Samuel Guttenplan (ed.), Mind and Language. Oxford University Press.
Intuitive semantics for first-degree entailments and 'coupled trees'.J. Michael Dunn - 1976 - Philosophical Studies 29 (3):149-168.